java.lang.NoClassDefFoundError: org/eclipse/mylyn/commons/core/StatusHandler
at org.eclipse.mylyn.internal.tasks.core.sync.SynchronizeQuerie sJob.run(SynchronizeQueriesJob.java:244)
at org.eclipse.mylyn.internal.tasks.core.sync.SynchronizeReposi toriesJob.updateQueries(SynchronizeRepositoriesJob.java:164)
at org.eclipse.mylyn.internal.tasks.core.sync.SynchronizeReposi toriesJob.run(SynchronizeRepositoriesJob.java:127)
at org.eclipse.core.internal.jobs.Worker.run(Worker.java:55)

<end error log>

One odd thing here is that during the time I've been getting this error, Mylyn has also been building contexts made up of random files. Files that I haven't touched, and that show no pattern of connection to anything I have touched, afaict. Not at all sure this is related.

Looks like you have an inconsistent Mylyn installation. This can happen
for any number of reasons. To resolve this situation you could try
checking for updates Help > Check for Updates. Alternatively, you could
remove the Mylyn features (Help > About Eclipse > Installation Details
button > Installed Software tab) and try installing again and hope that
the mirrors behave themselves.